In this section we restrict our discussion to the polynomial
hypergroups. First we consider polynomial
hypergroups in several variables which have been
already studied by several authors
(e.g. see [1]}, [2]}).
The translation operators of these hypergroups seem to be complicated, and the study of
their character amenability via the modified Reiter's condition, in
contrast to the one variable case [3]},
may
require sophisticated calculations.
In Theorem REF , however, we provide a necessary condition
to the \(\alpha \) -amenability of these hypergroups. Hence we point out that the majority of
common examples of polynomial hypergroups do not satisfy this condition.
